$(1)$ Please the following procedures and compare the cost of executing the same query.

$$

ALTER TABLE customer

ADD INDEX idx$\_$email $($email$)$;

$$

select customer$\_$id$,$ first$\_$name, last$\_$name, email

from customer

where email like $"$te$\%"$;

$$

$$

ALTER TABLE customer

DROP INDEX idx$\_$email;

$$

select customer$\_$id$,$ first$\_$name, last$\_$name, email

from customer

where email like $"$te$\%"$;

$$

$(2)$ Please explain how the balanced tree based index speeds up the data retrieval process.